Space of modular forms of level 666, weight 2, and Character 666.f

• Label: 666.2.f
• Level: $666$
• Weight: $2$
• Character orbit: 666.f
• Rep. character: $\chi_{666}(343,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $30$
• Newform subspaces: $10$
• Sturm bound: $228$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 37 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(228\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(666, [\chi])\).

	Total	New	Old
Modular forms	244	30	214
Cusp forms	212	30	182
Eisenstein series	32	0	32

Trace form

30 * q - q^2 - 15 * q^4 + 5 * q^5 + 2 * q^8 + 2 * q^10 - 8 * q^11 - 2 * q^13 + 8 * q^14 - 15 * q^16 - 3 * q^17 + 12 * q^19 + 5 * q^20 + 8 * q^22 - 24 * q^23 - 24 * q^25 - 4 * q^26 + 6 * q^29 + 40 * q^31 - q^32 - 9 * q^34 + 4 * q^35 - 23 * q^37 - 16 * q^38 - q^40 - 11 * q^41 - 16 * q^43 + 4 * q^44 + 16 * q^47 - 27 * q^49 + 12 * q^50 - 2 * q^52 - 2 * q^53 - 4 * q^55 - 4 * q^56 + 11 * q^58 + 16 * q^59 - 21 * q^61 + 30 * q^64 + 2 * q^65 - 8 * q^67 + 6 * q^68 - 16 * q^70 - 12 * q^71 - 4 * q^73 - 2 * q^74 + 12 * q^76 + 52 * q^77 + 4 * q^79 - 10 * q^80 - 38 * q^82 + 40 * q^83 + 54 * q^85 + 32 * q^86 - 16 * q^88 + 5 * q^89 + 28 * q^91 + 12 * q^92 - 12 * q^94 - 68 * q^95 - 46 * q^97 - 9 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(666, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
666.2.f.a	$666$	$2$	666.f	37.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None		✓			666.2.f.a	$2$	$1$	\(-1\)	\(0\)	\(-4\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-4\zeta_{6}q^{5}+\cdots\)
666.2.f.b	$666$	$2$	666.f	37.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None					74.2.c.a	$2$	$0$	\(-1\)	\(0\)	\(-1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}-\zeta_{6}q^{5}+q^{8}+\cdots\)
666.2.f.c	$666$	$2$	666.f	37.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None					222.2.e.b	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+\zeta_{6}q^{5}-2\zeta_{6}q^{7}+\cdots\)
666.2.f.d	$666$	$2$	666.f	37.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None					74.2.c.b	$2$	$0$	\(-1\)	\(0\)	\(3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{5}+\cdots\)
666.2.f.e	$666$	$2$	666.f	37.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None					222.2.e.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+3\zeta_{6}q^{7}-q^{8}+\cdots\)
666.2.f.f	$666$	$2$	666.f	37.c	$3$	$2$	$1$	$5.318$	\(\Q(\sqrt{-3}) \)	None		✓			666.2.f.a	$2$	$0$	\(1\)	\(0\)	\(4\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}-\zeta_{6}q^{4}+4\zeta_{6}q^{5}-3\zeta_{6}q^{7}+\cdots\)
666.2.f.g	$666$	$2$	666.f	37.c	$3$	$4$	$2$	$5.318$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None					222.2.e.c	$2$	$0$	\(-2\)	\(0\)	\(1\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-1+\beta _{1})q^{2}-\beta _{1}q^{4}+(\beta _{1}-\beta _{3})q^{5}+\cdots\)
666.2.f.h	$666$	$2$	666.f	37.c	$3$	$4$	$2$	$5.318$	\(\Q(\sqrt{-3}, \sqrt{11})\)	None		✓			666.2.f.h	$2$	$0$	\(-2\)	\(0\)	\(2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(1+\beta _{2})q^{5}+\cdots\)
666.2.f.i	$666$	$2$	666.f	37.c	$3$	$4$	$2$	$5.318$	\(\Q(\sqrt{-3}, \sqrt{11})\)	None		✓			666.2.f.h	$2$	$0$	\(2\)	\(0\)	\(-2\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{2}q^{2}+(-1-\beta _{2})q^{4}+(-1-\beta _{2}+\cdots)q^{5}+\cdots\)
666.2.f.j	$666$	$2$	666.f	37.c	$3$	$6$	$3$	$5.318$	6.0.4406832.1	None			✓		74.2.c.c	$2$	$0$	\(3\)	\(0\)	\(1\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1+\beta _{3})q^{2}+\beta _{3}q^{4}-\beta _{5}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(666, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(666, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(37, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(74, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(111, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(222, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(333, [\chi])\)\(^{\oplus 2}\)